We present an efficient approach to solve multi-dimensional time-dependent Schr?dinger equation(TDSE)in an intense laser field.In this approach,each spatial degree of freedom is treated as a distinguishable quasi-part...We present an efficient approach to solve multi-dimensional time-dependent Schr?dinger equation(TDSE)in an intense laser field.In this approach,each spatial degree of freedom is treated as a distinguishable quasi-particle.The non-separable Coulomb potential is regarded as a two-body operator between different quasi-particles.The time-dependent variational principle is used to derive the equations of motion.Then the high-order multi-dimensional problem is broken down into several lower-order coupled equations,which can be efficiently solved.As a demonstration,we apply this method to solve the two-dimensional TDSE.The accuracy is tested by comparing the direct solutions of TDSE using several examples such as the strong-field ionization and the high harmonic generation.The results show that the present method is much more computationally efficient than the conventional one without sacrificing accuracy.The present method can be straightforwardly extended to three-dimensional problems.Our study provides a flexible method to investigate the laser-atom interaction in the nonperturbative regime.展开更多
Coherent superposition of electronic states induces attosecond electron motion in molecules.We theoretically investigate the strong-field ionization of this superposition state by numerically solving the time-dependen...Coherent superposition of electronic states induces attosecond electron motion in molecules.We theoretically investigate the strong-field ionization of this superposition state by numerically solving the time-dependent Schrodinger equation.In the obtained photoelectron momentum distribution,an intriguing bifurcation structure appears in the strong-field holographic interference pattern.We demonstrate that this bifurcation structure directly provides complete information about the status of the transient wave function of the superposition state:the horizontal location of the bifurcation in the momentum distribution reveals the relative phase of the involved components of the superposition state and the vertical position indicates the relative coefficient.Thus,this bifurcation structure takes a snapshot of the transient electron wave packet of the superposition state and provides an intuitive way to monitor electron motion in molecules.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12204545 and 12274294)the Program for NUE independent research and development。
文摘We present an efficient approach to solve multi-dimensional time-dependent Schr?dinger equation(TDSE)in an intense laser field.In this approach,each spatial degree of freedom is treated as a distinguishable quasi-particle.The non-separable Coulomb potential is regarded as a two-body operator between different quasi-particles.The time-dependent variational principle is used to derive the equations of motion.Then the high-order multi-dimensional problem is broken down into several lower-order coupled equations,which can be efficiently solved.As a demonstration,we apply this method to solve the two-dimensional TDSE.The accuracy is tested by comparing the direct solutions of TDSE using several examples such as the strong-field ionization and the high harmonic generation.The results show that the present method is much more computationally efficient than the conventional one without sacrificing accuracy.The present method can be straightforwardly extended to three-dimensional problems.Our study provides a flexible method to investigate the laser-atom interaction in the nonperturbative regime.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11874163,11604108,and 11604388)the Program for HUST Academic Frontier Youth Teamthe Fundamental Research Funds for the Central Universities,China(HUST No.2017KFXKJC002)。
文摘Coherent superposition of electronic states induces attosecond electron motion in molecules.We theoretically investigate the strong-field ionization of this superposition state by numerically solving the time-dependent Schrodinger equation.In the obtained photoelectron momentum distribution,an intriguing bifurcation structure appears in the strong-field holographic interference pattern.We demonstrate that this bifurcation structure directly provides complete information about the status of the transient wave function of the superposition state:the horizontal location of the bifurcation in the momentum distribution reveals the relative phase of the involved components of the superposition state and the vertical position indicates the relative coefficient.Thus,this bifurcation structure takes a snapshot of the transient electron wave packet of the superposition state and provides an intuitive way to monitor electron motion in molecules.
